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In this paper we discuss a model describing global behavior of the two phase incompressible flow in fractured porous media. The fractured media is regarded as a porous medium consisting of two superimposed continua, a connected fracture…

Analysis of PDEs · Mathematics 2014-03-05 Mladen Jurak , Leonid Pankratov , Anja Vrbaški

The flow of fluids within porous rocks is an important process with numerous applications in Earth sciences. Modeling the compaction-driven fluid flow requires the solution of coupled nonlinear partial differential equations that account…

Geophysics · Physics 2026-03-03 Simon Boisserée , Evangelos Moulas , Markus Bachmayr

Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability…

Numerical Analysis · Mathematics 2024-01-30 K. B. Nakshatrala

Upscaling unsaturated flow in fractured rock remains challenging because fractures and matrix often exhibit sharply contrasting hydraulic behaviors across saturation states. Here, we demonstrate that unsaturated flow undergoes a transition…

Geophysics · Physics 2026-04-02 Muhammad R. Andiva , Chuanyin Jiang , Martin Ziegler , Qinghua Lei

The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously…

Analysis of PDEs · Mathematics 2020-08-21 Fernando A Morales , Luis C Aristizábal

An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume…

Computational Physics · Physics 2021-03-15 Francisco J. Carrillo , Ian C. Bourg , Cyprien Soulaine

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…

The fracturing-flooding technology is a new process for the development of low-permeability oil reservoirs, achieving a series of successful applications in oilfield production. However, existing numerical simulation methods for pressure…

Optimization and Control · Mathematics 2026-05-28 Xiang Wang , Wenjie Yu , Yixin Xie , Yanfeng He , Hui Xu , Xianxiang Chu , Changfu Li

In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with…

Numerical Analysis · Mathematics 2018-11-08 Andrés Arrarás , Francisco J. Gaspar , Laura Portero , Carmen Rodrigo

Mixed-dimensional mathematical models for flow in fractured media have been prevalent in the modeling community for almost two decades, utilizing the explicit representation of fractures by lower-dimensional manifolds embedded in the…

We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of a tensile or shear…

Computational Physics · Physics 2017-04-26 Maria Laura De Bellis , Gabriele Della Vecchia , Michael Ortiz , Anna Pandolfi

A three-dimensional Multiphysics Lattice Discrete Particle Model (M-LDPM) framework is formulated to investigate the fracture permeability behavior of shale. The framework features a dual lattice system mimicking the mesostructure of the…

Geophysics · Physics 2019-02-12 Weixin Li , Xinwei Zhou , J. William Carey , Luke P. Frash , Gianluca Cusatis

In this paper we give a new proof of the homogenization result for an immiscible incompressible two-phase flow in double porosity media obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli\'c (1996) and in the paper…

Analysis of PDEs · Mathematics 2016-08-23 Brahim Amaziane , Mladen Jurak , Leonid Pankratov , Anja Vrbaski

Fluid flow in rough fractures and the coupling with the mechanical behaviour of the fractures pose great difficulties for numerical modeling approaches, due to complex fracture surface topographies, the non-linearity of hydromechanical…

Computational Physics · Physics 2020-03-17 Cyrill von Planta , Daniel Vogler , Xiaoqing Chen , Maria G. C. Nestola , Martin O. Saar , Rolf Krause

The paper is devoted to the derivation, by linearization, of simplified (fully homogenized) homogenized models of an immiscible incompressible two-phase flow in double porosity media in the case of thin fissures. In a simplified dual…

Analysis of PDEs · Mathematics 2022-11-14 Mladen Jurak , Leonid Pankratov , Anja Vrbaški

Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many…

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools…

Geophysics · Physics 2016-05-26 D. Roubinet , N. Linde , D. Jougnot , J. Irving

Through this research, embedded synthetic fracture networks in rock masses are studied. To analysis the fluid flow complexity in fracture networks with respect to the variation of connectivity patterns, two different approaches are…

Computational Engineering, Finance, and Science · Computer Science 2012-02-23 H. O. Ghaffari , M. H. B. Nasseri , R. P. Young

Loss of circulation while drilling is a challenging problem that may interrupt operations, reduce efficiency, and may contaminate the subsurface. When a drilled borehole intercepts conductive faults or fractures, lost circulation manifests…

Geophysics · Physics 2021-05-28 Rami Albattat , Hussein Hoteit

We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…

Numerical Analysis · Mathematics 2020-06-15 Juan Galvis , Eduardo Abreu , Ciro Diaz , Jonh Perez